22 lines
600 B
Markdown
22 lines
600 B
Markdown
$$n=N_c\cdot e^{\frac{-(E_c-E_F)}{kT}}$$
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$$p=N_v\cdot e^{\frac{-(E_F-E_v)}{kT}}$$
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- $E_c$ is the position of the conduction band minimum
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- $E_v$ is the position of the valence band maxmimum
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- $k$ is Boltzmann's constant
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- $N_x$ are the effective density of states
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$$np=n_i^2$$
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- $n_i$ = Intrinsic carrier concentration
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$$n_i=\sqrt{N_cN_v}e^{\frac{-E_g}{2kt}}$$
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- $E_g$ = Band Gap = $E_c-E_v$
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## Substitutional Doping
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- Donated electrons are delocalised
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- Ions are immobile
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$$N_c \equiv 2 \left[ \frac{2\pi m_nkT}{h^2}\right]^{3/2}$$
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$$N_v \equiv 2 \left[ \frac{2\pi m_pkT}{h^2}\right]^{3/2}$$
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